falafronk

94 Questions
0 Answers

-1

27

0

+359

Circles

The two circles below are externally tangent. A common external tangent intersects line $PQ$ at $R.$ Find $QR.$

falafronk Mar 25, 2024

-1

34

0

+359

Circle

A circular table is pushed into a corner of the room, where two walls meet at a right angle. A point $P$ on the edge of the table (as shown below) has a distance of $10$ from one wall, and a distance of $13$ from the other wall. Find the radius read more ..

falafronk Mar 25, 2024

-1

42

0

+359

help maximum

Let x and y be nonnegative real numbers. If x^2 + 3y^2 = 18, then find the maximum value of x + y.

falafronk Mar 25, 2024

-1

23

0

+359

Minimum

Let x and y be nonnegative real numbers. If xy = \frac{2}{5}, then find the minimum value of 6x + \frac{3}{5y}.

falafronk Mar 25, 2024

-1

27

1

+359

Temperature

The temperature of a point (x,y) in the plane is given by the expression x^2 + y^2 - 4x + 2y - 12x + 14y + 26. What is the temperature of the coldest point in the plane?

falafronk Mar 25, 2024

-1

27

1

+359

Geometry

In triangle $ABC,$ let the angle bisectors be $\overline{BY}$ and $\overline{CZ}$. Given $AB = 12$, $AY = 12$, and $CY = 6$, find $BZ$.

falafronk Mar 25, 2024

-1

19

1

+359

Geometry

In triangle $ABC,$ let the angle bisectors be $\overline{BY}$ and $\overline{CZ}$. Given $AB = 12$, $AY = 12$, and $CY = 6$, find $BC$.

falafronk Mar 25, 2024

-1

21

1

+359

Square

In the diagram below, P is a point inside square ABCD. Find x.

falafronk Mar 25, 2024

-1

29

1

+359

Geometry

Two lines $p$ and $q$ intersect at $X$. The angle between lines $p$ and $q$ is $45^\circ$. Let $A$ be a point inside the $45^\circ$ angle formed by $p$ and $q$. Let $B$ be the reflection of $A$ through line $p,$ and let $C$ be the reflection read more ..

falafronk Mar 25, 2024

-1

25

0

+359

help how do you do this

In rectangle $EFGH$, let $M$ be the midpoint of $\overline{EF}$, and let $X$ be a point such that $MH = MX$, as shown below. If $\angle EFH = 30^\circ$ and $\angle MHX = 60^\circ,$ then find $\angle XHG,$ in degrees.

falafronk Mar 25, 2024